Establishing the symmetry of the Cooper pair wave function is the
pivotal step to understand a superconductor. It not only determines the
macroscopic phenomenology, but it also narrows down the microscopic mechanism
of the pairing state. Arguably the strongest evidence that cuprate-based
high-temperature superconductors are governed by an electronic mechanism
is the observation of the \(d_{x^{2}-y^{2}}\)  symmetry of the pair
wave function [1]}, [2]}. \(\mathrm {Sr}_{2}\mathrm {Ru}\mathrm {O}_{4}\)  is
a layered perovskite superconductor that is iso-structural to La\(_{2}\) CuO\(_{4}\)  [3]}.
Given the crossover from incoherent to coherent transport as function
of temperature, \(\mathrm {Sr}_{2}\mathrm {Ru}\mathrm {O}_{4}\)  is—just like the
cuprates—governed by strong electronic correlations [4]}. However,
early on it was advocated that the more appropriate analogue for the
origin and symmetry of the pairing state might be \(^{3}\) He [5]}, [6]}.
Indeed, in distinction to the cuprates, broken time-reversal symmetry
below \(T_{c}\)  was observed in muon spin relaxation [7]}, [8]}
and polar Kerr effect [9]} measurements, reminiscent of
the \(p_{x} + ip_{y}\)  pairing state of the A-phase of \(^{3}\) He.
